曲线曲面扩散流的周长缩减面积保持算法
A perimeter-decreasing and area-conserving algorithm for surface diffusion flow of curves
摘要：
基于一种新的弱列式和一种新的时间推进格式，提出了一种全离散有限元法，用于二维平面内闭曲线的表面扩散流动。证明了该方法可以在离散层次上同时保持两种几何结构，曲线的周长随时间减小，而由曲线包围的面积保持不变。数值算例证明了该方法的收敛性和保持两种几何结构的有效性。
英文摘要：
A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can preserve two geometric structures simultaneously at the discrete level, i.e., the perimeter of the curve decreases in time while the area enclosed by the curve is conserved. Numerical examples are provided to demonstrate the convergence of the proposed method and the effectiveness of the method in preserving the two geometric structures.
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